SU (9) Family Unification S. Nandi Oklahoma State University and - - PowerPoint PPT Presentation

SU(9) Family Unification

• S. Nandi

Oklahoma State University and Oklahoma Center for High Energy Physics

(in collaboration with J. Dent and T. W. Kephart) arXiv: 0908.3915[hep-ph] (to appear in Phys. Lett. B) Talk at PHENO 2010, Madison, Wisconsin, May, 2010

• S. Nandi

SU(9) Family Unification

Goals

To present a SU(9) model of family unification with 3 light chiral families. To provide a natural hierarchy for the charged fermion masses and mixings. To link the scale of the tiny neutrino masses with the hierarchy of the quark masses and mixings.

• S. Nandi

SU(9) Family Unification

Outline of Talk

Introduction Model and the Formalism Phenomenological Implications Conclusions and Outlook

• S. Nandi

SU(9) Family Unification

Introduction

3 light families of quarks and leptons 5 orders of magnitude hierarchy among the charged fermion masses 2 orders of magnitude hierarchy among the quark mixing angles Neutrino masses are 7 orders of magnitude smaller that the lightest charged fermion masses

• S. Nandi

SU(9) Family Unification

Introduction

Our approach Use SU(5) as one family GUT Enlarge the symmetry to SU(N), N > 5, to include more families Use only anti-symmetric representations of SU(9) ⇒ only 5, ¯ 5, 10, ¯ 10, 1 Choose a set of anti-symmetric representations such that ⇒ 3(¯ 5 + 10) + n1(5 + ¯ 5) + n2(10 + ¯ 10) + n3(1) (5 + ¯ 5), (10 + ¯ 10), and 1 in the GUT scale ⇒ only 3(¯ 5 + 10) light families of fermions

• S. Nandi

SU(9) Family Unification

Introduction

Questions: How to generate fermion masses and mixing hierarchy? How to suppress FCNC processes? How to explain mν ≪ mq, ml?

• r how to generate mNR/MGUT = 10−2?
• S. Nandi

SU(9) Family Unification

Introduction

Our philosophy Use additional discrete symmetries to arrange the hierarchy of the Yukawa couplingss Only top quark have dim 4 Yukawa coupling Yukawa couplings of the lighter quarks will appear successively as higher dimensional operators Link the neutrino mass scale to the suppression of these Yukawa couplings

• S. Nandi

SU(9) Family Unification

Model & Formalism

Our concrete model Gauge Symmetry: SU(9) Use additional discrete symmetries, Z2, Z′

2, Z′′2, and Z3 to

constrain the Yukawa couplings suitably Only top quark has dim 4 Yukawa coupling Yukawa couplings of all other quarks are successively higher dimensional (hence suppressed), and are constrained by the above symmetries Supression factor, ε = VS/VGUT where VS = VeV of an SU(5) singlet Higgs field, and VGUT = GUT scale VeV.

• S. Nandi

SU(9) Family Unification

Model & Formalism

F = 126 + 84 + 2(36) + 14(¯ 9) Note that this assignment is anomaly free. 126 → 5 + 4(10) + 6(10) + 4(¯ 5) + 1 84 → 10 + 4(10) + 6(5) + 4(1) 36 → 10 + 4(5) + 6(1) ¯ 9 → ¯ 5 + 4(1) Hence the complete set of fermions in the model is F = 3(10 + ¯ 5)F + 15(5 + ¯ 5)F + 7(10 + 10)F + 73(1)F . ⇒ 3 light families of fermions.

• S. Nandi

SU(9) Family Unification

Model & Formalism

Assignment of three chiral families: 3rd family : (1263)F → tL, tR, bL ¯ 93 → bR 2nd family : 842 → cL, cR, sL ¯ 92 → sR 1st family : 361 → uL, uR, dL ¯ 91 → dR In addition, the Higgs represetations that we shall use are 36H, 36′H, 36′′H, 9H, and 315H.

• S. Nandi

SU(9) Family Unification

Model & Formalism

Charges under the discrete symmetries: Z2 Z′

2

Z′′

2

Z3 (1263)F −1 (842)F −1 (361)F −1 (93)F α (92)F −1 (91)F −1 −1 α 36H 36′

H

−1 36′′

H

α 9H −1 −1 315H

• S. Nandi

SU(9) Family Unification

Model& and the Formalism

Allowed Yukawa interactions: D = 4 :

• tt :

(126F )2 315H D = 5 :      cc : (842)F (842)F 36H 315H ct = tc : (1263)F (842)F [36H 315H + (315)2

H]

bb : (1263)F (¯ 93)F 36′

H 36′′ H

D = 6 :                      tu = ut : (1263)F (361)F [(36H)2 + (36′

H)2] (36H)

cu = uc : (842)F (361)F 36H [(9H)2 + (315H)2] bs : (1263)F (¯ 92)F 36H 36′

H 9H

sb : (¯ 93)F (842)F (36′′

H)2 36′ H

ss : (842)F (¯ 92)F 36′

H 9H 315H

bd : (1263)F (¯ 91)F (36′′

H)2 9H

• S. Nandi

SU(9) Family Unification

Model& and the Formalism

Allowed Yukawa interactions (continued): D = 7 :            uu : (361)F (361)F (9H)2 315H 36H dd : (361)F (¯ 91)F 36′

H (36′′ H)2 9H

db : (361)F (¯ 93)F 36′

H (36′′ H)2 315H

sd : (842)F (¯ 91)F 36H 36′

H 36′′ H 9H

• S. Nandi

SU(9) Family Unification

Phenomenological Implications

Up and down quark mass matrices Mu =   hu

11ε3

hu

12ε2

hu

13ε2

hu

21ε2

hu

22ε

hu

23ε

hu

31ε2

hu

32ε

hu

33

  v. Md =   hd

11ε3

hd

12ε3

hd

13ε3

hd

21ε3

hd

22ε2

hd

23ε2

hd

31ε2

hd

32ε2

hd

33ε

  v .

• S. Nandi

SU(9) Family Unification

Phenomenological Implications

Quark and lepton masses, CKM mixing, FCNC and Higgs Decays Existence of 3 light families from a gauge SU(9) family symmetry Parameters of the model: hu

ij, hd ij,ε = VS/VGUT

With choices hu

ij, hd ij ∼ O(1), and ε ∼ 1/50, good agreement

with all the quark and charged lepton masses. No SM singlet Higgs at the EW scale (Our singlet Higgs are close to the GUT scale) Yukawa coupling matrices and the mass matrices are proportional ⇒ No FCNC as in SM SM Higgs boson decays are identical to those in SM

• S. Nandi

SU(9) Family Unification

Phenomenological Implications

Neutrino masses and mixings ¯ 9 of SU(9) ⇒ ¯ 5F + 4(1)F Singlet fermions are unavoidable Existence of RH neutrinos are required in our model this is similar to SO(10) GUT, but we have a family unification gauge symmetry Mass scale for these RH neutrinos are linked to the suppression factor needed to explain charged fermion mass hierarchy and CKM mixings, ε = VS/VGUT ⇒ MR ∼ 1014 GeV, as required to explain the observed light neutrino masses via see-saw

• S. Nandi

SU(9) Family Unification

Conclusions

Presented a family unification model with three light chiral families Based on SU(9) gauge symmetry with additional discrete symmetries Generate the hierarchy of quark and charged lepton masses, and CKM mixings SM singlet neutrinos are unavoidable Links the scale of the RH singlet neutrinos ∼ 1014 GeV to quark mass hierarchy and mixings

• S. Nandi

SU(9) Family Unification